Chiral Anomaly in Contorted Spacetimes

Abstract

The Dirac equation in Riemann-Cartan spacetimes with torsion is reconsidered. As is well-known, only the axial covector torsion $A$, a one-form, couples to massive Dirac fields. Using diagrammatic techniques, we show that besides the familiar Riemannian term only the Pontrjagin type four-form $dA\wedge dA$ does arise additionally in the chiral anomaly, but not the Nieh-Yan term $d^{\ast }A$, as has been claimed recently. Implications for cosmic strings in Einstein-Cartan theory as well as for Ashtekar's canonical approach to quantum gravity are discussed.

17 pages, REVTEX

References in corpus (1)

• Topological Invariants, Instantons and Chiral Anomaly on Spaces with Torsion

Cited by in corpus (10)

• Gravitational Goldstone fields from affine gauge theory
• Comment on: Topological Invariants, instantons, and the chiral anomaly on spaces with torsion
• On the chiral anomaly in non-Riemannian spacetimes
• Einstein-Cartan gravity, Asymptotic Safety, and the running Immirzi parameter
• Topological magnetotorsional effect in Weyl semimetals
• Conservation laws in the teleparallel theory of gravity
• Translations and dynamics
• de Sitter group and Einstein-Hilbert Lagrangian
• Phonon helicity and Nieh-Yan Anomaly in the Kramers-Weyl semimetals of Chiral Crystals
• Torsion, Chern-Simons Term and Diffeomorphism Invariance